Re: [Phys-l] Teaching Special Relativity

["Richard Tarara" <rbtarara@sprynet.com>]

----- Original Message ----- 

> On Jul 3, 2009, at 12:55 PM, John Mallinckrodt wrote:
>
> > I don't think or claim that it is a pedagogical disaster to say that
> > it might seem "as if" the mass of the object were increasing with
> > velocity.  But I do think that it approaches pedagogical malpractice
> > not to point out in something like the same breath that it should not
> > be taken seriously because it leads to all sorts of other problems.
> > Furthermore, it seems to me to be a simple and appropriate matter to
> > go on to point out that the more appropriate way to view the result
> > is either

Thanks John,

I have no problem (as I do in other areas such as gravity and weight) 
pointing out that we are using a simple model that has been superseded in 
more recent times, but is sufficient for talking about (or calculating for 
that matter) the observed phenomena.  So I am not ashamed to say that the 
observations of high speed objects from our normal (nearly inertial--and 
taken to be such) frame of reverence can be characterized as moving clocks 
run slow, moving masses increase, and moving lengths contract along the 
direction of motion.  I would add that somewhat more sophisticated analyses, 
especially those taken from the frame of the moving object, would describe 
the phenomena differently, but we have neither the time nor quite the 
mathematical tools to go there.  The travelling twin IS younger--to us (stay 
at homes)--his 'clock' has run slower to our perceptions, the momentum of 
the electrons we bent in the lab has increased much more than the velocity 
but from our measurements of velocity and our ideas of momentum the effect 
is that the mass of the electron has (seemingly) increased,  and for 
complete consistency (in our frame) the lengths must have contracted.

I can't see that this is any 'worse' than teaching Newtonian gravity and 
calculating with Newtonian gravity.  It might not give us the right answer 
in all situations, but it remains a useful 'first model' in most cases.  I 
don't hear the complaints that we are 300 years out of tune or 
intellectually dishonest or just plain stupid for doing so.  ;-)

****************

> This begs for another question. What is more important, for non-
> physics majors, "more elegant worldview" or "understanding of everyday
> phenomena" ?

> Ludwik

At one level (especially the gen-ed level) I would say simply knowing that 
some of the phenomena exist is the goal.  My students really don't have a 
clue about special relativity and many really are fascinated by the 'Twins' 
phenomena and are amazed that there is real evidence for what we present 
hypothetically being true.  No need to complicate this with gory 
details--the travelling twin comes back and is younger than his brother. 
The effect is seen in moving sub-atomic particles and was once confirmed by 
moving atomic clocks around the world in opposite directions with the clocks 
showing a difference in time on being brought back together that agreed with 
the predictions of Special relativity.  It is somewhat more difficult with 
my gen-ed students (easier with the science students) to talk about the 
bending of high speed particles but I try with an animation of the 
trajectories through the bending magnet set using classical theory and then 
relativistic theory.  Talking about contractions involves using some 
whimsical animations showing what should be seen from the fixed frame and 
the moving frame and then falling back on non-simultaneity (also described 
through some animations) to 'hand wave' that both observations can be shown 
to be consistent when analyzed fully in the appropriate frames.   This is 
really about all that I feel is possible and appropriate for gen-ed 
students, but the goal here is to get across the idea that Newtonian 
Mechanics, while good for 95% of our daily needs, simply doesn't work at 
high speeds and that the seemingly 'strange' phenomena associated with such 
high speed motion can be fully understood with the more modern relativistic 
models that physicists now use.  We do a little more with the (non physics) 
science students--but not that much.  Any who might pursue more physics 
studies will end up taking a 'modern' physics course where special 
relativity will be dealt with more fully and from a totally updated 
perspective (at least I assume today's modern texts do so--haven't looked at 
any in years.)

Rick

Richard W. Tarara
Professor of Physics
Department of Chemistry & Physics
Saint Mary's College
Notre Dame, IN 46556